Process engineers overseeing manufacturing processes analyze collected data related to the manufacturing process to detect faults and monitor conditions associated with the process. The analysis may be performed dynamically in conjunction with an ongoing process, or it may performed “off line” in an effort to improve the process for the next performance. Technological advances in the form of more sophisticated statistical analysis programs, faster computers and advanced process databases have contributed to increased efforts in this area by process engineers.
There has also been considerable and growing interest among researchers and practitioners in the application of process monitoring to batch processes. Batch processes typically display a non-steady state during processing. Economically the growth in interest in process monitoring this has been driven by the value of early detection and diagnosis of batch process disturbances (since many batch processes often involve high value products which in many cases have to be discarded if the batch does not follow an ‘in control’ trajectory). One source of the growing interest has been the lack of on-line critical product quality measurements for many batch processes. The inability to produce product quality on line measurements has sharpened the need for technology which can use existing indirect measurements of product quality to provide warning of deviant process conditions during the execution of the batch, while there is still time to take a mid-course correction.
The most widespread and established application of process visualization technology has been in its most basic form, where process operators view electronic versions of Statistical Process Control (or SPC) charts for a selection of measured process variables. Anomalous or upset process conditions are detected by recognizing when the time series shown on those charts deviate from some defined control region. The simplicity of the SPC approach has contributed to its popularity, but there are two major practical drawbacks that have limited its effectiveness:
In most manufacturing processes the measured variables are related to each other through physical interaction, so that there is not necessarily a direct relationship between a particular variable exiting its control limits and the root cause of a process upset. Additionally, most manufacturing operations have hundreds or more measured variables, making it impossible for a human operator to monitor each and every measurement using a separate SPC chart.
These limitations regarding SPC charts have prompted the development of other approaches to process condition monitoring based on Principle Component Analysis (PCA) and Partial Least Squares (PLS) as well as other multivariate statistical methods. These alternative techniques essentially detect the existence of a process upset by monitoring certain common factors (subsequently referred to herein as ‘scores’), chosen to represent significant components of the overall process variability. An upset condition is flagged when the vector of scores exits some defined control region subsequently labeled the ‘in-control’ and ‘control’ region. There are established mathematical methods for detecting the incidence of this type of ‘out of control’ event, but visualization of the behavior of the scores relative to the ‘in control’ region can offer physical insight into the process behavior and the cause of an upset, especially in cases where the scores are imbued with some physical meaning. Conventionally, two approaches are used to perform visualization of the behavior of scores relative to control regions whenever 3 or more scores are involved:
Each scalar score component is viewed separately from the other scores but relative to the limits of the ‘in control’ region as they apply that component. The resulting monitoring display consists of n SPC strip charts (where n is the number of score components). Conceptually this is the equivalent of plotting a one dimensional cross-section of an n-dimensional score space viewed relative to upper and lower bounds defined by a one dimensional cross-section of the n-dimensional solid that defines the ‘in control’ region. In cases where the process condition is represented by 3 scores, a graphical projection method is often used to provide a 2 dimensional depiction of the scores and the 3 dimensional solid representing the control region (usually an ellipsoid). Those skilled in the art will recognize that 2 or fewer scores can be monitored with a two dimensional planar plot of the score trajectories and ‘in-control’ region without requiring any of the visualization features described in this disclosure.
One drawback of the first approach (where each coordinate is viewed separately) is that it ignores the real dependence of the ‘in-control’ boundaries on a combination of the coordinates, making it difficult to assess the in-control state of the process without considering all the score values simultaneously. A consequence of ignoring the effect of combining coordinates is that separate strip plots of each score can disguise the severity of an impending process upset. FIG. 1A shows a graphical projection 1 of a sequence of three scores representing the state of a monitored process where the coordinates have already been combined. The evolution of the score trajectory is represented by a line 2 and the coordinates of the most recent 3 scores are indicated by a dot 4 (it should be understood throughout the discussion herein that many of the described visualization techniques are performed using colors on an electronic display to increase visual contrast). The translucent semi-ellipsoid represents the bottom half of the ‘in control’ region enclosing score values defined by normal operation. It is apparent from the graphical projection 1 that the trend is towards an imminent exit of the score plot control region, and impending detection of a process upset. However, the corresponding strip chart plots 8, 10 and 12 of the individual scores and their individual control regions are shown in FIG. 1B (each individual control region is defined by the values of that coordinate within the ellipsoidal control region shown in FIG. 1b.) The individual strip charts 8, 10 and 12 give no indication of the impending upset since each score trajectory is well within the interior of each ‘in control’ band.
It should be noted that the concept of scores as defined in PCA/PLS process monitoring (as the coefficients describing the state of the process in the subspace of principle components) can be extended to any application where the process condition is summarized by a numerical vector. Other examples, which are based on physical rather than statistical process models, might include applications where the process condition is represented by estimates of physical quantities such as stored heat, new inflow, heat flux, etc.
In cases where the scores may be associated with physical quantities relating to process operation, the relative position of the score trajectory and the ‘in-control’ region provides an indication of what corrective action is needed to bring the process back into control. While strip chart plots such as those shown in FIG. 1B indicate the relative adjustments of each score required to move the process back into the ‘in-control’ region, the geometrical intuition provided by graphical projections usually provides faster human perception of the relative adjustments of the three score values. The graphical projection approach has therefore increasingly been used to try to give a more geometrical view of the scores and the ‘in control’ region. In general however even this is not sufficient to completely convey either the process state or its trend.
Although more informative than the strip charts, a static graphical projection suffers from a number of drawbacks. Conventional graphical projections cannot unambiguously convey the position of the scores in a 3-dimensional space since the computer screen is essentially a 2-dimensional depiction and each point on a graphical projection defines a line in 3 dimensions. The user must also be able to move the viewpoint of the display in order to create a sequence of graphical projections so as to clarify the ambiguity of multiple positions in 3 dimensional space corresponding to a single point depiction on a 2 dimensional graphical projection. The ability to shift viewpoint in order to view processed data is missing in conventional methods. Additionally, the representation of the control region fails to allow viewing of both the interior and exterior of the ‘in control’ region in order to display whether and where score trajectories enter or exit. Another significant shortcoming of conventional process visualization methods is that there are generally more than three scores, in which case a 3 dimensional graphical projection will not capable of representing the 4 or more score coordinates. Conventional process visualization techniques lack the ability to combine graphical methods with exploration methods in order to allow the user to vary the geometry of the projection and so gain insight into the relationship between the scores and the ‘in control’ region.
An additional problem with conventional graphical visualization methods arises when there is a need to visualize regions of scores represented as 3 dimensional or higher bodies (or geometrical shapes) as opposed to the type of score trajectories shown in FIG. 1A and FIG. 1B. The need to visualize three dimensional or higher bodies with a three dimensional control region arises in batch multi-way process monitoring where the scores are not known precisely during the batch and consequently score vectors are characterized as regions of uncertainty rather than single points. Also, ‘what if’ or scenario analysis analyses where measured variables are allowed to take values over some set of possibilities, and the potential interaction of the score loci with the ‘in control’ boundary must be viewed to asses the affect of each of the possibilities also requires the need to visualize the interaction of three dimensional or larger solids in space. In these situations inference depends on assessing the overlap of 3 dimensional or larger solids in space. Without the ability to vary the viewpoint parallax makes the process of determining the relative positions of the solids difficult and one dimensional cross sections often yield misleading results.
Unlike continuous processes, batch processes are usually designed to have varying conditions over the course of their run, and consequently any assessment of the batch condition must take into account the entire course history rather than just the current conditions. The standard approach to batch process monitoring is to use extensions of multivariate statistical methods for continuous processes (known as multi-way PCA and multi-way PLS) adapted to handle non-steady state conditions. Multi-way methods work by considering each new observation of each measured variable during the batch as a distinct variable, and the entire batch as a single observation of that collection of variables. Thus, the history of all the measured variables during the batch is reduced to a single vector representing one extended observation, and the overall batch state of the batch by the vector of scores calculated for that observation. Viewing observations of the same measurement at different times as distinct variables allows multi-way methods to treat different times differently, in effect recognizing that different periods of the batch trajectory are more or less impact on final product quality. However, computation of the score vector requires the complete batch history, which presents a challenge for in-course assessment of the state of the batch, because the observation set required for estimation of scores is not complete while the batch is running. Consequently, forecasts of future measurements are employed (extending from the current time until the end of the batch) to complete the multi-way observation vector and calculate estimates of the likely end of batch score vector. Since the future measurement trajectories are uncertain, the calculated end point scores are no longer defined by a vector but rather by a probability distribution.
When these probability distributions are viewed geometrically they define a region of probable values in score space rather than a single point. Assessment of whether the final score vector will likely end up in the control region then amounts to judging whether there is significant overlap between the region of end point uncertainty and the region defining the score values of ‘in-control’ batches. While probability distributions of score vectors for in-process batches have been derived by various methods in the research literature, there has been no development of techniques for their visualization other than for one score component at a time. Thus the potential for misleading and confusing results stemming from one-dimensional visualization that was discussed above is further heightened for the case of batch process monitoring attempting the more complex task of assessing the relative position of two regions (score uncertainty region which is evolving in time as more of the measurement trajectories become available and the ‘in-control’ region).